Now showing items 1-20 of 22

• #### Analytic Varieties with Finite Volume Amoebas are Algebraic ﻿

[OWP-2011-33] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
In this paper, we study the amoeba volume of a given $k$-dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba ...
• #### Criteria for Algebraicity of Analytic Functions ﻿

[OWP-2018-25] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-12)
We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ...
• #### Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps ﻿

[OWP-2018-20] (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-08)
Demailly's conjecture, which is a consequence of the Green-Griffiths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ...
• #### Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps (Revised Edition) ﻿

[OWP-2018-20.2] (Mathematisches Forschungsinstitut Oberwolfach, 2020-01-23)
Demailly's conjecture, which is a consequence of the Green-Griffths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ...
• #### Freeness of Multi-Reflection Arrangements via Primitive Vector Fields ﻿

[OWP-2017-10] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-20)
In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ...
• #### A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables ﻿

[OWP-2019-02] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-11)
For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
• #### Global Variants of Hartogs' Theorem ﻿

[OWP-2018-24] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-06)
Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ...
• #### Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants ﻿

[OWP-2017-35] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-13)
We find new bi-Lipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature.
• #### Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements ﻿

[OWP-2017-14] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-30)
Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger ...
• #### Milnor fibre homology via deformation ﻿

[OWP-2015-22] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
In case of one-dimensional singular locus, we use deformations in order toget refined information about the Betti numbers of the Milnor fibre.
• #### A new counting function for the zeros of holomorphic curves ﻿

[OWP-2009-25] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-18)
Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the ...
• #### Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into a projective variety intersecting hypersurfaces ﻿

[OWP-2010-19] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
In 1985, Fujimoto established a non-integrated defect relation for meromorphic maps of complete Kähler manifolds into the complex projective space intersecting hyperplanes in general position. In this paper, we generalize ...
• #### Numerical Invariants and Moduli Spaces for Line Arrangements ﻿

[OWP-2017-02] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-01)
Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane ...
• #### On the Directionally Newton-non-degenerate Singularities of Complex Hypersurfaces ﻿

[OWP-2008-16] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We introduce a minimal generalization of Newton-non-degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newton-non-degenerate if the local embedded ...
• #### On the geometry of regular maps from a quasi-projective surface to a curve ﻿

[OWP-2013-03] (Mathematisches Forschungsinstitut Oberwolfach, 2013-03-14)
We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X.
• #### On the non-analyticity locus of an arc-analytic function ﻿

[OWP-2009-03] (Mathematisches Forschungsinstitut Oberwolfach, 2009-02-21)
A function is called arc-analytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arc-analytic functions that are not real analytic. Arc analytic functions appear ...
• #### On the δ=const Collisions of Singularities of Complex Plane Curves ﻿

[OWP-2008-15] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ...
• #### Rational Approximation on Products of Planar Domains ﻿

[OWP-2016-05] (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)
We consider $A(\Omega)$, the Banach space of functions $f$ from $\overline{\Omega}=\prod_{i \in I} \overline{U_i}$ to $\mathbb{C}$ that are continuous with respect to the product topology and separately holomorphic, where ...
• #### Real Analyticity is Concentrated in Dimension 2 ﻿

[OWP-2018-23] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-05)
We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ...
• #### Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces ﻿

[OWP-2011-38] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove ...